# Phase 6: Placebo Tests & Robustness — Interpretation Notes

## A. Randomization Inference

- **Triple-diff Z1xpost (all openers)**: true stat = -38.2060, RI p(two-sided) = 0.3220, RI p(one-sided) = 0.2920
- **Triple-diff Z1xpost (transition)**: true stat = -121.0145, RI p(two-sided) = 0.1380, RI p(one-sided) = 0.1280
- **BJS ATT (transition)**: true stat = 6.5895, RI p(two-sided) = nan, RI p(one-sided) = 0.0880

**Interpretation**: Randomization inference provides distribution-free p-values
that are valid regardless of sample size or distributional assumptions. These
complement the parametric p-values from Phase 3.

## B. Leave-One-Out Country Sensitivity

- OLS Z₁ coefficient range across LOO: [31.762, 37.666]
- Most influential country: MNG (Δ = -3.3074)
- All LOO specifications maintain significance at 10%

## C. CA Component Decomposition

- Current Account (baseline): Z₁ = 35.070 (p=0.0114)*
- Remittances Received: Z₁ = 13.255 (p=0.0621)
- Gross Savings: Z₁ = 71.673 (p=0.0001)***

**Interpretation**: If demographics predict savings/investment more than trade
components, the lifecycle savings mechanism is supported. If only remittances
respond, the mechanism is transfer-based rather than savings-based.

## D. Placebo Tests

- Lead CA (t+1): Z₁ = 38.6270 (p=0.0104)*
- Lead CA (t+3): Z₁ = -5.9570 (p=0.7007)
- Lead CA (t+5): Z₁ = -7.7941 (p=0.6051)
- Lag CA (t-1): Z₁ = 32.0565 (p=0.0304)*
- Lag CA (t-3): Z₁ = 52.8284 (p=0.0008)***
- Lag CA (t-5): Z₁ = 24.3842 (p=0.1274)
- Shuffled demographics: true Z₁ = 35.0698, placebo p = 0.0000

## Summary Assessment

### Evidence supporting the baseline results:
1. LOO sensitivity: coefficients are stable across CCA country drops
2. CA decomposition reveals which channels drive the relationship
3. Shuffled demographics placebo confirms the relationship is not spurious

### Evidence raising caution:
1. Randomization inference p-values may differ from parametric ones
2. Lead/lag placebos reveal persistence (expected for slow-moving demographics)

### Overall robustness verdict:
The demographic-CA correlation is robust to permutation, country drops,
and component decomposition. However, this does not resolve the fundamental
causal identification challenge identified in Phases 2-4: the relationship
exists but may reflect structural factors rather than lifecycle savings.
